Source code for pyscf.hessian.rks

#!/usr/bin/env python
# Copyright 2014-2019 The PySCF Developers. All Rights Reserved.
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
#     http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
#
# Author: Qiming Sun <osirpt.sun@gmail.com>
#

'''
Non-relativistic RKS analytical Hessian
'''


import numpy
from pyscf import lib
from pyscf.lib import logger
from pyscf.hessian import rhf as rhf_hess
from pyscf.grad import rks as rks_grad
from pyscf.dft import numint


# import pyscf.grad.rks to activate nuc_grad_method method
from pyscf.grad import rks  # noqa


[docs] def partial_hess_elec(hessobj, mo_energy=None, mo_coeff=None, mo_occ=None, atmlst=None, max_memory=4000, verbose=None): log = logger.new_logger(hessobj, verbose) time0 = t1 = (logger.process_clock(), logger.perf_counter()) mol = hessobj.mol mf = hessobj.base ni = mf._numint if mf.nlc or ni.libxc.is_nlc(mf.xc): raise NotImplementedError('RKS Hessian for NLC functional') if mo_energy is None: mo_energy = mf.mo_energy if mo_occ is None: mo_occ = mf.mo_occ if mo_coeff is None: mo_coeff = mf.mo_coeff if atmlst is None: atmlst = range(mol.natm) nao, nmo = mo_coeff.shape mocc = mo_coeff[:,mo_occ>0] dm0 = numpy.dot(mocc, mocc.T) * 2 omega, alpha, hyb = ni.rsh_and_hybrid_coeff(mf.xc, spin=mol.spin) hybrid = ni.libxc.is_hybrid_xc(mf.xc) de2, ej, ek = rhf_hess._partial_hess_ejk(hessobj, mo_energy, mo_coeff, mo_occ, atmlst, max_memory, verbose, with_k=hybrid) de2 += ej - hyb * ek # (A,B,dR_A,dR_B) mem_now = lib.current_memory()[0] max_memory = max(2000, mf.max_memory*.9-mem_now) veff_diag = _get_vxc_diag(hessobj, mo_coeff, mo_occ, max_memory) if hybrid and omega != 0: with mol.with_range_coulomb(omega): vk1 = rhf_hess._get_jk(mol, 'int2e_ipip1', 9, 's2kl', ['jk->s1il', dm0])[0] veff_diag -= (alpha-hyb)*.5 * vk1.reshape(3,3,nao,nao) vk1 = None t1 = log.timer_debug1('contracting int2e_ipip1', *t1) aoslices = mol.aoslice_by_atom() vxc = _get_vxc_deriv2(hessobj, mo_coeff, mo_occ, max_memory) for i0, ia in enumerate(atmlst): shl0, shl1, p0, p1 = aoslices[ia] shls_slice = (shl0, shl1) + (0, mol.nbas)*3 veff = vxc[ia] if hybrid and omega != 0: with mol.with_range_coulomb(omega): vk1, vk2 = rhf_hess._get_jk(mol, 'int2e_ip1ip2', 9, 's1', ['li->s1kj', dm0[:,p0:p1], # vk1 'lj->s1ki', dm0 ], # vk2 shls_slice=shls_slice) veff -= (alpha-hyb)*.5 * vk1.reshape(3,3,nao,nao) veff[:,:,:,p0:p1] -= (alpha-hyb)*.5 * vk2.reshape(3,3,nao,p1-p0) t1 = log.timer_debug1('range-separated int2e_ip1ip2 for atom %d'%ia, *t1) with mol.with_range_coulomb(omega): vk1 = rhf_hess._get_jk(mol, 'int2e_ipvip1', 9, 's2kl', ['li->s1kj', dm0[:,p0:p1]], # vk1 shls_slice=shls_slice)[0] veff -= (alpha-hyb)*.5 * vk1.transpose(0,2,1).reshape(3,3,nao,nao) t1 = log.timer_debug1('range-separated int2e_ipvip1 for atom %d'%ia, *t1) vk1 = vk2 = None de2[i0,i0] += numpy.einsum('xypq,pq->xy', veff_diag[:,:,p0:p1], dm0[p0:p1])*2 for j0, ja in enumerate(atmlst[:i0+1]): q0, q1 = aoslices[ja][2:] de2[i0,j0] += numpy.einsum('xypq,pq->xy', veff[:,:,q0:q1], dm0[q0:q1])*2 for j0 in range(i0): de2[j0,i0] = de2[i0,j0].T log.timer('RKS partial hessian', *time0) return de2
[docs] def make_h1(hessobj, mo_coeff, mo_occ, chkfile=None, atmlst=None, verbose=None): mol = hessobj.mol if atmlst is None: atmlst = range(mol.natm) nao, nmo = mo_coeff.shape mocc = mo_coeff[:,mo_occ>0] dm0 = numpy.dot(mocc, mocc.T) * 2 hcore_deriv = hessobj.base.nuc_grad_method().hcore_generator(mol) mf = hessobj.base ni = mf._numint ni.libxc.test_deriv_order(mf.xc, 2, raise_error=True) omega, alpha, hyb = ni.rsh_and_hybrid_coeff(mf.xc, spin=mol.spin) hybrid = ni.libxc.is_hybrid_xc(mf.xc) mem_now = lib.current_memory()[0] max_memory = max(2000, mf.max_memory*.9-mem_now) h1ao = _get_vxc_deriv1(hessobj, mo_coeff, mo_occ, max_memory) aoslices = mol.aoslice_by_atom() for i0, ia in enumerate(atmlst): shl0, shl1, p0, p1 = aoslices[ia] shls_slice = (shl0, shl1) + (0, mol.nbas)*3 if hybrid: vj1, vj2, vk1, vk2 = \ rhf_hess._get_jk(mol, 'int2e_ip1', 3, 's2kl', ['ji->s2kl', -dm0[:,p0:p1], # vj1 'lk->s1ij', -dm0 , # vj2 'li->s1kj', -dm0[:,p0:p1], # vk1 'jk->s1il', -dm0 ], # vk2 shls_slice=shls_slice) veff = vj1 - hyb * .5 * vk1 veff[:,p0:p1] += vj2 - hyb * .5 * vk2 if omega != 0: with mol.with_range_coulomb(omega): vk1, vk2 = \ rhf_hess._get_jk(mol, 'int2e_ip1', 3, 's2kl', ['li->s1kj', -dm0[:,p0:p1], # vk1 'jk->s1il', -dm0 ], # vk2 shls_slice=shls_slice) veff -= (alpha-hyb) * .5 * vk1 veff[:,p0:p1] -= (alpha-hyb) * .5 * vk2 else: vj1, vj2 = rhf_hess._get_jk(mol, 'int2e_ip1', 3, 's2kl', ['ji->s2kl', -dm0[:,p0:p1], # vj1 'lk->s1ij', -dm0 ], # vj2 shls_slice=shls_slice) veff = vj1 veff[:,p0:p1] += vj2 h1ao[ia] += veff + veff.transpose(0,2,1) h1ao[ia] += hcore_deriv(ia) if chkfile is None: return h1ao else: for ia in atmlst: lib.chkfile.save(chkfile, 'scf_f1ao/%d'%ia, h1ao[ia]) return chkfile
XX, XY, XZ = 4, 5, 6 YX, YY, YZ = 5, 7, 8 ZX, ZY, ZZ = 6, 8, 9 XXX, XXY, XXZ, XYY, XYZ, XZZ = 10, 11, 12, 13, 14, 15 YYY, YYZ, YZZ, ZZZ = 16, 17, 18, 19 def _get_vxc_diag(hessobj, mo_coeff, mo_occ, max_memory): mol = hessobj.mol mf = hessobj.base if hessobj.grids is not None: grids = hessobj.grids else: grids = mf.grids if grids.coords is None: grids.build(with_non0tab=True) nao, nmo = mo_coeff.shape ni = mf._numint xctype = ni._xc_type(mf.xc) shls_slice = (0, mol.nbas) ao_loc = mol.ao_loc_nr() vmat = numpy.zeros((6,nao,nao)) if xctype == 'LDA': ao_deriv = 2 for ao, mask, weight, coords \ in ni.block_loop(mol, grids, nao, ao_deriv, max_memory): rho = ni.eval_rho2(mol, ao[0], mo_coeff, mo_occ, mask, xctype) vxc = ni.eval_xc_eff(mf.xc, rho, 1, xctype=xctype)[1] wv = weight * vxc[0] aow = numint._scale_ao(ao[0], wv) for i in range(6): vmat[i] += numint._dot_ao_ao(mol, ao[i+4], aow, mask, shls_slice, ao_loc) aow = None elif xctype == 'GGA': def contract_(mat, ao, aoidx, wv, mask): aow = numint._scale_ao(ao[aoidx[0]], wv[1]) aow+= numint._scale_ao(ao[aoidx[1]], wv[2]) aow+= numint._scale_ao(ao[aoidx[2]], wv[3]) mat += numint._dot_ao_ao(mol, aow, ao[0], mask, shls_slice, ao_loc) ao_deriv = 3 for ao, mask, weight, coords \ in ni.block_loop(mol, grids, nao, ao_deriv, max_memory): rho = ni.eval_rho2(mol, ao[:4], mo_coeff, mo_occ, mask, xctype) vxc = ni.eval_xc_eff(mf.xc, rho, 1, xctype=xctype)[1] wv = weight * vxc #:aow = numpy.einsum('npi,np->pi', ao[:4], wv[:4]) aow = numint._scale_ao(ao[:4], wv[:4]) for i in range(6): vmat[i] += numint._dot_ao_ao(mol, ao[i+4], aow, mask, shls_slice, ao_loc) contract_(vmat[0], ao, [XXX,XXY,XXZ], wv, mask) contract_(vmat[1], ao, [XXY,XYY,XYZ], wv, mask) contract_(vmat[2], ao, [XXZ,XYZ,XZZ], wv, mask) contract_(vmat[3], ao, [XYY,YYY,YYZ], wv, mask) contract_(vmat[4], ao, [XYZ,YYZ,YZZ], wv, mask) contract_(vmat[5], ao, [XZZ,YZZ,ZZZ], wv, mask) rho = vxc = wv = aow = None elif xctype == 'MGGA': def contract_(mat, ao, aoidx, wv, mask): aow = numint._scale_ao(ao[aoidx[0]], wv[1]) aow+= numint._scale_ao(ao[aoidx[1]], wv[2]) aow+= numint._scale_ao(ao[aoidx[2]], wv[3]) mat += numint._dot_ao_ao(mol, aow, ao[0], mask, shls_slice, ao_loc) ao_deriv = 3 for ao, mask, weight, coords \ in ni.block_loop(mol, grids, nao, ao_deriv, max_memory): rho = ni.eval_rho2(mol, ao[:10], mo_coeff, mo_occ, mask, xctype) vxc = ni.eval_xc_eff(mf.xc, rho, 1, xctype=xctype)[1] wv = weight * vxc wv[4] *= .5 # for the factor 1/2 in tau #:aow = numpy.einsum('npi,np->pi', ao[:4], wv[:4]) aow = numint._scale_ao(ao[:4], wv[:4]) for i in range(6): vmat[i] += numint._dot_ao_ao(mol, ao[i+4], aow, mask, shls_slice, ao_loc) contract_(vmat[0], ao, [XXX,XXY,XXZ], wv, mask) contract_(vmat[1], ao, [XXY,XYY,XYZ], wv, mask) contract_(vmat[2], ao, [XXZ,XYZ,XZZ], wv, mask) contract_(vmat[3], ao, [XYY,YYY,YYZ], wv, mask) contract_(vmat[4], ao, [XYZ,YYZ,YZZ], wv, mask) contract_(vmat[5], ao, [XZZ,YZZ,ZZZ], wv, mask) aow = [numint._scale_ao(ao[i], wv[4]) for i in range(1, 4)] for i, j in enumerate([XXX, XXY, XXZ, XYY, XYZ, XZZ]): vmat[i] += numint._dot_ao_ao(mol, ao[j], aow[0], mask, shls_slice, ao_loc) for i, j in enumerate([XXY, XYY, XYZ, YYY, YYZ, YZZ]): vmat[i] += numint._dot_ao_ao(mol, ao[j], aow[1], mask, shls_slice, ao_loc) for i, j in enumerate([XXZ, XYZ, XZZ, YYZ, YZZ, ZZZ]): vmat[i] += numint._dot_ao_ao(mol, ao[j], aow[2], mask, shls_slice, ao_loc) vmat = vmat[[0,1,2, 1,3,4, 2,4,5]] return vmat.reshape(3,3,nao,nao) def _make_dR_rho1(ao, ao_dm0, atm_id, aoslices, xctype): p0, p1 = aoslices[atm_id][2:] ngrids = ao[0].shape[0] if xctype == 'GGA': rho1 = numpy.zeros((3,4,ngrids)) elif xctype == 'MGGA': rho1 = numpy.zeros((3,5,ngrids)) ao_dm0_x = ao_dm0[1][:,p0:p1] ao_dm0_y = ao_dm0[2][:,p0:p1] ao_dm0_z = ao_dm0[3][:,p0:p1] # (d_X \nabla mu) dot \nalba nu DM_{mu,nu} rho1[0,4] += numpy.einsum('pi,pi->p', ao[XX,:,p0:p1], ao_dm0_x) rho1[0,4] += numpy.einsum('pi,pi->p', ao[XY,:,p0:p1], ao_dm0_y) rho1[0,4] += numpy.einsum('pi,pi->p', ao[XZ,:,p0:p1], ao_dm0_z) rho1[1,4] += numpy.einsum('pi,pi->p', ao[YX,:,p0:p1], ao_dm0_x) rho1[1,4] += numpy.einsum('pi,pi->p', ao[YY,:,p0:p1], ao_dm0_y) rho1[1,4] += numpy.einsum('pi,pi->p', ao[YZ,:,p0:p1], ao_dm0_z) rho1[2,4] += numpy.einsum('pi,pi->p', ao[ZX,:,p0:p1], ao_dm0_x) rho1[2,4] += numpy.einsum('pi,pi->p', ao[ZY,:,p0:p1], ao_dm0_y) rho1[2,4] += numpy.einsum('pi,pi->p', ao[ZZ,:,p0:p1], ao_dm0_z) rho1[:,4] *= .5 else: raise RuntimeError ao_dm0_0 = ao_dm0[0][:,p0:p1] # (d_X \nabla_x mu) nu DM_{mu,nu} rho1[:,0] = numpy.einsum('xpi,pi->xp', ao[1:4,:,p0:p1], ao_dm0_0) rho1[0,1]+= numpy.einsum('pi,pi->p', ao[XX,:,p0:p1], ao_dm0_0) rho1[0,2]+= numpy.einsum('pi,pi->p', ao[XY,:,p0:p1], ao_dm0_0) rho1[0,3]+= numpy.einsum('pi,pi->p', ao[XZ,:,p0:p1], ao_dm0_0) rho1[1,1]+= numpy.einsum('pi,pi->p', ao[YX,:,p0:p1], ao_dm0_0) rho1[1,2]+= numpy.einsum('pi,pi->p', ao[YY,:,p0:p1], ao_dm0_0) rho1[1,3]+= numpy.einsum('pi,pi->p', ao[YZ,:,p0:p1], ao_dm0_0) rho1[2,1]+= numpy.einsum('pi,pi->p', ao[ZX,:,p0:p1], ao_dm0_0) rho1[2,2]+= numpy.einsum('pi,pi->p', ao[ZY,:,p0:p1], ao_dm0_0) rho1[2,3]+= numpy.einsum('pi,pi->p', ao[ZZ,:,p0:p1], ao_dm0_0) # (d_X mu) (\nabla_x nu) DM_{mu,nu} rho1[:,1] += numpy.einsum('xpi,pi->xp', ao[1:4,:,p0:p1], ao_dm0[1][:,p0:p1]) rho1[:,2] += numpy.einsum('xpi,pi->xp', ao[1:4,:,p0:p1], ao_dm0[2][:,p0:p1]) rho1[:,3] += numpy.einsum('xpi,pi->xp', ao[1:4,:,p0:p1], ao_dm0[3][:,p0:p1]) # *2 for |mu> DM <d_X nu| return rho1 * 2 def _d1d2_dot_(vmat, mol, ao1, ao2, mask, ao_loc, dR1_on_bra=True): shls_slice = (0, mol.nbas) if dR1_on_bra: # (d/dR1 bra) * (d/dR2 ket) for d1 in range(3): for d2 in range(3): vmat[d1,d2] += numint._dot_ao_ao(mol, ao1[d1], ao2[d2], mask, shls_slice, ao_loc) else: # (d/dR2 bra) * (d/dR1 ket) for d1 in range(3): for d2 in range(3): vmat[d1,d2] += numint._dot_ao_ao(mol, ao1[d2], ao2[d1], mask, shls_slice, ao_loc) def _get_vxc_deriv2(hessobj, mo_coeff, mo_occ, max_memory): mol = hessobj.mol mf = hessobj.base if hessobj.grids is not None: grids = hessobj.grids else: grids = mf.grids if grids.coords is None: grids.build(with_non0tab=True) nao, nmo = mo_coeff.shape ni = mf._numint xctype = ni._xc_type(mf.xc) aoslices = mol.aoslice_by_atom() shls_slice = (0, mol.nbas) ao_loc = mol.ao_loc_nr() dm0 = mf.make_rdm1(mo_coeff, mo_occ) vmat = numpy.zeros((mol.natm,3,3,nao,nao)) ipip = numpy.zeros((3,3,nao,nao)) if xctype == 'LDA': ao_deriv = 1 for ao, mask, weight, coords \ in ni.block_loop(mol, grids, nao, ao_deriv, max_memory): rho = ni.eval_rho2(mol, ao[0], mo_coeff, mo_occ, mask, xctype) vxc, fxc = ni.eval_xc_eff(mf.xc, rho, 2, xctype=xctype)[1:3] wv = weight * vxc[0] aow = [numint._scale_ao(ao[i], wv) for i in range(1, 4)] _d1d2_dot_(ipip, mol, aow, ao[1:4], mask, ao_loc, False) ao_dm0 = numint._dot_ao_dm(mol, ao[0], dm0, mask, shls_slice, ao_loc) wf = weight * fxc[0,0] for ia in range(mol.natm): p0, p1 = aoslices[ia][2:] # *2 for \nabla|ket> in rho1 rho1 = numpy.einsum('xpi,pi->xp', ao[1:,:,p0:p1], ao_dm0[:,p0:p1]) * 2 # aow ~ rho1 ~ d/dR1 wv = wf * rho1 aow = [numint._scale_ao(ao[0], wv[i]) for i in range(3)] _d1d2_dot_(vmat[ia], mol, ao[1:4], aow, mask, ao_loc, False) ao_dm0 = aow = None for ia in range(mol.natm): p0, p1 = aoslices[ia][2:] vmat[ia,:,:,:,p0:p1] += ipip[:,:,:,p0:p1] elif xctype == 'GGA': ao_deriv = 2 for ao, mask, weight, coords \ in ni.block_loop(mol, grids, nao, ao_deriv, max_memory): rho = ni.eval_rho2(mol, ao[:4], mo_coeff, mo_occ, mask, xctype) vxc, fxc = ni.eval_xc_eff(mf.xc, rho, 2, xctype=xctype)[1:3] wv = weight * vxc wv[0] *= .5 aow = rks_grad._make_dR_dao_w(ao, wv) _d1d2_dot_(ipip, mol, aow, ao[1:4], mask, ao_loc, False) ao_dm0 = [numint._dot_ao_dm(mol, ao[i], dm0, mask, shls_slice, ao_loc) for i in range(4)] wf = weight * fxc for ia in range(mol.natm): dR_rho1 = _make_dR_rho1(ao, ao_dm0, ia, aoslices, xctype) wv = numpy.einsum('xyg,sxg->syg', wf, dR_rho1) wv[:,0] *= .5 for i in range(3): aow = rks_grad._make_dR_dao_w(ao, wv[i]) rks_grad._d1_dot_(vmat[ia,i], mol, aow, ao[0], mask, ao_loc, True) aow = [numint._scale_ao(ao[:4], wv[i,:4]) for i in range(3)] _d1d2_dot_(vmat[ia], mol, ao[1:4], aow, mask, ao_loc, False) ao_dm0 = aow = None for ia in range(mol.natm): p0, p1 = aoslices[ia][2:] vmat[ia,:,:,:,p0:p1] += ipip[:,:,:,p0:p1] vmat[ia,:,:,:,p0:p1] += ipip[:,:,p0:p1].transpose(1,0,3,2) elif xctype == 'MGGA': XX, XY, XZ = 4, 5, 6 YX, YY, YZ = 5, 7, 8 ZX, ZY, ZZ = 6, 8, 9 ao_deriv = 2 for ao, mask, weight, coords \ in ni.block_loop(mol, grids, nao, ao_deriv, max_memory): rho = ni.eval_rho2(mol, ao[:10], mo_coeff, mo_occ, mask, xctype) vxc, fxc = ni.eval_xc_eff(mf.xc, rho, 2, xctype=xctype)[1:3] wv = weight * vxc wv[0] *= .5 wv[4] *= .25 aow = rks_grad._make_dR_dao_w(ao, wv) _d1d2_dot_(ipip, mol, aow, ao[1:4], mask, ao_loc, False) aow = [numint._scale_ao(ao[i], wv[4]) for i in range(4, 10)] _d1d2_dot_(ipip, mol, [aow[0], aow[1], aow[2]], [ao[XX], ao[XY], ao[XZ]], mask, ao_loc, False) _d1d2_dot_(ipip, mol, [aow[1], aow[3], aow[4]], [ao[YX], ao[YY], ao[YZ]], mask, ao_loc, False) _d1d2_dot_(ipip, mol, [aow[2], aow[4], aow[5]], [ao[ZX], ao[ZY], ao[ZZ]], mask, ao_loc, False) ao_dm0 = [numint._dot_ao_dm(mol, ao[i], dm0, mask, shls_slice, ao_loc) for i in range(4)] wf = weight * fxc for ia in range(mol.natm): dR_rho1 = _make_dR_rho1(ao, ao_dm0, ia, aoslices, xctype) wv = numpy.einsum('xyg,sxg->syg', wf, dR_rho1) wv[:,0] *= .5 wv[:,4] *= .5 # for the factor 1/2 in tau for i in range(3): aow = rks_grad._make_dR_dao_w(ao, wv[i]) rks_grad._d1_dot_(vmat[ia,i], mol, aow, ao[0], mask, ao_loc, True) aow = [numint._scale_ao(ao[:4], wv[i,:4]) for i in range(3)] _d1d2_dot_(vmat[ia], mol, ao[1:4], aow, mask, ao_loc, False) aow = [numint._scale_ao(ao[1], wv[i,4]) for i in range(3)] _d1d2_dot_(vmat[ia], mol, [ao[XX], ao[XY], ao[XZ]], aow, mask, ao_loc, False) aow = [numint._scale_ao(ao[2], wv[i,4]) for i in range(3)] _d1d2_dot_(vmat[ia], mol, [ao[YX], ao[YY], ao[YZ]], aow, mask, ao_loc, False) aow = [numint._scale_ao(ao[3], wv[i,4]) for i in range(3)] _d1d2_dot_(vmat[ia], mol, [ao[ZX], ao[ZY], ao[ZZ]], aow, mask, ao_loc, False) for ia in range(mol.natm): p0, p1 = aoslices[ia][2:] vmat[ia,:,:,:,p0:p1] += ipip[:,:,:,p0:p1] vmat[ia,:,:,:,p0:p1] += ipip[:,:,p0:p1].transpose(1,0,3,2) return vmat def _get_vxc_deriv1(hessobj, mo_coeff, mo_occ, max_memory): mol = hessobj.mol mf = hessobj.base if hessobj.grids is not None: grids = hessobj.grids else: grids = mf.grids if grids.coords is None: grids.build(with_non0tab=True) nao, nmo = mo_coeff.shape ni = mf._numint xctype = ni._xc_type(mf.xc) aoslices = mol.aoslice_by_atom() shls_slice = (0, mol.nbas) ao_loc = mol.ao_loc_nr() dm0 = mf.make_rdm1(mo_coeff, mo_occ) v_ip = numpy.zeros((3,nao,nao)) vmat = numpy.zeros((mol.natm,3,nao,nao)) max_memory = max(2000, max_memory-vmat.size*8/1e6) if xctype == 'LDA': ao_deriv = 1 for ao, mask, weight, coords \ in ni.block_loop(mol, grids, nao, ao_deriv, max_memory): rho = ni.eval_rho2(mol, ao[0], mo_coeff, mo_occ, mask, xctype) vxc, fxc = ni.eval_xc_eff(mf.xc, rho, 2, xctype=xctype)[1:3] wv = weight * vxc[0] aow = numint._scale_ao(ao[0], wv) rks_grad._d1_dot_(v_ip, mol, ao[1:4], aow, mask, ao_loc, True) ao_dm0 = numint._dot_ao_dm(mol, ao[0], dm0, mask, shls_slice, ao_loc) wf = weight * fxc[0,0] for ia in range(mol.natm): p0, p1 = aoslices[ia][2:] # First order density = rho1 * 2. *2 is not applied because + c.c. in the end rho1 = numpy.einsum('xpi,pi->xp', ao[1:,:,p0:p1], ao_dm0[:,p0:p1]) wv = wf * rho1 aow = [numint._scale_ao(ao[0], wv[i]) for i in range(3)] rks_grad._d1_dot_(vmat[ia], mol, aow, ao[0], mask, ao_loc, True) ao_dm0 = aow = None elif xctype == 'GGA': ao_deriv = 2 for ao, mask, weight, coords \ in ni.block_loop(mol, grids, nao, ao_deriv, max_memory): rho = ni.eval_rho2(mol, ao[:4], mo_coeff, mo_occ, mask, xctype) vxc, fxc = ni.eval_xc_eff(mf.xc, rho, 2, xctype=xctype)[1:3] wv = weight * vxc wv[0] *= .5 rks_grad._gga_grad_sum_(v_ip, mol, ao, wv, mask, ao_loc) ao_dm0 = [numint._dot_ao_dm(mol, ao[i], dm0, mask, shls_slice, ao_loc) for i in range(4)] wf = weight * fxc for ia in range(mol.natm): dR_rho1 = _make_dR_rho1(ao, ao_dm0, ia, aoslices, xctype) wv = numpy.einsum('xyg,sxg->syg', wf, dR_rho1) wv[:,0] *= .5 aow = [numint._scale_ao(ao[:4], wv[i,:4]) for i in range(3)] rks_grad._d1_dot_(vmat[ia], mol, aow, ao[0], mask, ao_loc, True) ao_dm0 = aow = None elif xctype == 'MGGA': if grids.level < 5: logger.warn(mol, 'MGGA Hessian is sensitive to dft grids.') ao_deriv = 2 for ao, mask, weight, coords \ in ni.block_loop(mol, grids, nao, ao_deriv, max_memory): rho = ni.eval_rho2(mol, ao[:10], mo_coeff, mo_occ, mask, xctype) vxc, fxc = ni.eval_xc_eff(mf.xc, rho, 2, xctype=xctype)[1:3] wv = weight * vxc wv[0] *= .5 wv[4] *= .5 # for the factor 1/2 in tau rks_grad._gga_grad_sum_(v_ip, mol, ao, wv, mask, ao_loc) rks_grad._tau_grad_dot_(v_ip, mol, ao, wv[4], mask, ao_loc, True) ao_dm0 = [numint._dot_ao_dm(mol, ao[i], dm0, mask, shls_slice, ao_loc) for i in range(4)] wf = weight * fxc for ia in range(mol.natm): dR_rho1 = _make_dR_rho1(ao, ao_dm0, ia, aoslices, xctype) wv = numpy.einsum('xyg,sxg->syg', wf, dR_rho1) wv[:,0] *= .5 wv[:,4] *= .25 aow = [numint._scale_ao(ao[:4], wv[i,:4]) for i in range(3)] rks_grad._d1_dot_(vmat[ia], mol, aow, ao[0], mask, ao_loc, True) for j in range(1, 4): aow = [numint._scale_ao(ao[j], wv[i,4]) for i in range(3)] rks_grad._d1_dot_(vmat[ia], mol, aow, ao[j], mask, ao_loc, True) ao_dm0 = aow = None for ia in range(mol.natm): p0, p1 = aoslices[ia][2:] vmat[ia,:,p0:p1] += v_ip[:,p0:p1] vmat[ia] = -vmat[ia] - vmat[ia].transpose(0,2,1) return vmat
[docs] class Hessian(rhf_hess.Hessian): '''Non-relativistic RKS hessian''' _keys = set(['grids', 'grid_response']) def __init__(self, mf): rhf_hess.Hessian.__init__(self, mf) self.grids = None self.grid_response = False partial_hess_elec = partial_hess_elec make_h1 = make_h1
from pyscf import dft dft.rks.RKS.Hessian = dft.rks_symm.RKS.Hessian = lib.class_as_method(Hessian)